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Some properties of set-valued stochastic integrals of multiprocesses with finite Castaing representations

Kisielewicz M.

Commentationes Mathematicae

2013

Vol. 53, No. 2

113--126

The paper contains new properties of set-valued stochastic integrals defined as multifunctions with subtrajectory integrals equal to closed decomposable hulls of functional set-valued integrals defined in the author paper [8]. In particular, it is proved that such defined integrals for set-valued predictable square integrably bounded processes having finite Castaing representations are square integrably bounded. Up to now this property has not been proved. Unfortunately, in the general case the above boundedness problem is still open.

A Common Fixed Point Theorem for Set-valued Contraction Mappings in Menger Space

Pant B. D., Chauhan S., Kumar S.

Commentationes Mathematicae

2012

Vol. 52, [Z] 1

61-71

The aim of this paper is to prove a common fixed point theorem for even number of single-valued and two set-valued mappings in complete Menger space using implicit relation. Our result improves and extends the result of Chen and Chang [Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006, Art. ID 75931, 15 pp].

The stability of the quadratic equation for set valued mappings

Czerwik S., Dłutek K.

Zeszyty Naukowe. Matematyka - Fizyka / Politechnika Śląska

1999

z. 84

105-116

In the paper we consider the problem of the Ulam-Hyers and Rassias types of stability of the quadratic functional equation for set-valued functions.

W artykule rozpatrywany jest problem stabilności równania funkcjonałów kwadratowych dla funkcji wielowartościowych.